GBM

GBM

intersection of ideals for zero-dimensional schemes

Syntax

GBM(L: LIST): IDEAL

Description

***** NOT YET IMPLEMENTED *****

This function computes the intersection of ideals corresponding to zero-dimensional schemes: GBM is for affine schemes, and HGBM for projective schemes. The list L must be a list of ideals. The function IntersectList should be used for computing the intersection of a collection of general ideals.

The name GBM comes from the name of the algorithm used: Generalized Buchberger-Moeller.

Example

/**/  Use P ::= QQ[x,y,z];
/**/  I1 := IdealOfPoints(P, mat([[1,2,1], [0,1,0]])); -- a simple affine scheme
/**/  I2 := IdealOfPoints(P, mat([[1,1,1], [2,0,1]]))^2;-- another affine scheme

***** NOT YET IMPLEMENTED *****
  GBM([I1, I2]);                                  -- intersect the ideals
ideal(xz + yz - z^2 - x - y + 1,
 z^3 - 2z^2 + z,
 yz^2 - 2yz - z^2 + y + 2z - 1,
 y^2z - y^2 - yz + y,
 xy^2 + y^3 - 2x^2 - 5xy - 5y^2 + 2z^2 + 8x + 10y - 4z - 6,
 x^2y - y^3 + 2x^2 + 2xy + 4y^2 - 3z^2 - 8x - 8y + 6z + 5,
 x^3 + y^3 - 7x^2 - 5xy - 4y^2 + 5z^2 + 16x + 10y - 10z - 7,
 y^4 - 2y^3 - 4x^2 - 8xy - 3y^2 + 4z^2 + 16x + 16y - 8z - 12)
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See Also